From the knitting process oil circular machines there is obtained, as is known, a fabric component having a tubular shape which is led and progressively wound onto a winding roller arranged in the lower part of tlie machine. However, it is well known to persons skilled in the art that with the winding onto the winding roller of the tubular fabric, two folds are inevitably formed along two generators on opposite sides of the tubular component and produce an opposite effect during treatments, processing and subsequent use of tile fabric. Even when the tubular fabric component is being cut along its generator, the problem is only partially resolved since, with the winding of the fabric component onto a winding roller, even if open on one side, a longitudinal fold is always formed, however, on the other side of the fabric.